Diet + exercise is hurting my wife's health

Patient

Q: My wife is on a diet + exercise plan because she wants to lose weight. We both are sports and fitness lovers so we've read a lot calorie counts and all that; however, there's something I cannot find a straight answer about:

I know for a woman her age and height she should have a daily intake of 1950 calories; I also know that she should have an intake of 1450 if she wants to lose half a kilogram per week.
On the other hand, I know she SHOULD NOT have a daily calorie intake lower than 1100.

As a result of her plan, she is in fact eating less than 1450 calories and she's burning about 400 through exercise.
So, her daily math is taking her to a number lower than 1100; for example...
Monday: Intake 1230 - exercise 460 = 770
Tuesday: Intake 1140 - exercise 260 =880
Wednesday: Intake 1390 - exercise 680 = 710

She insists the procedure is not harmful because her intake is above 1100

My question is: is that procedure healthy for her or should she make sure THE RESULT of the equation is above 1100 and not only the intake?
I'm really worried about her. I truly believe her hair loss, fatigue, excessive hunger and (sometimes) disorganized menstrual period are the result of this plan.
Please help.

Symptoms:  Fatigue, irritability, excessive hair loss, excessive hunger
Doctor

A:   This question is currently in queue and will be answered shortly by one of our doctors. In the meantime you may browse our library of answered questions by clicking here.

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